Calculation of microscopic exchange interactions and modelling of macroscopic magnetic properties in molecule-based magnets

Abstract

The state-of-the-art theoretical evaluation and rationalization of the magnetic interactions (J(AB)) in molecule-based magnets is discussed in this critical review, focusing first on isolated radical···radical pair interactions and afterwards on how these interactions cooperate in the solid phase. Concerning isolated radical pairwise magnetic interactions, an initial analysis is done on qualitative grounds, concentrating also on the validity of the most commonly used models to predict their size and angularity (namely, McConnell-I and McConnell-II models, overlap of magnetic orbitals,…). The failure of these models, caused by their oversimplified description of the magnetic interactions, prompted the introduction of quantitative approaches, whose basic principles and relative quality are also evaluated. Concerning the computation of magnetic interactions in solids, we resort to a sum of pairwise magnetic interactions within the Heisenberg Hamiltonian framework, and follow the First-principles Bottom-Up procedure, which allows the accurate study of the magnetic properties of any molecule-based magnet in an unbiased way. The basic principles of this approach are outlined, applied in detail to a model system, and finally demonstrated to properly describe the magnetic properties of molecule-based systems that show a variety of magnetic topologies, which range from 1D to 3D (152 references).

Exchange constants in molecule-based magnets derived from density functional methods

“…If this is not the case, then the error in this assumption is absorbed into the value of the exchange constant that is derived. More specifically, we map the magnetic centers of the system to an Ising Hamiltonian [3][4][5] …”

“…In the DFA [3][4][5], the system is divided into pairs of magnetic centers corresponding to magnetic exchange pathways. In many cases [5] the value of the exchange constant linking those centers can be described accurately using only the two centers and their corresponding ligands.…”

“…Previously, Journet-Somoza et al [11] (hereafter JS) used the DFA [3,4] to show that small changes in bond lengths between temperatures of 158 and 2 K cause the magnetic exchange along interchain pathways to become significant at the lower temperature. The crystal structure at 2 K is not expected to change significantly as the temperature is lowered further, and so they argue that the topology of magnetic exchange paths that they find is valid below T N = 110 mK.…”

“…This involves determining the relative energies of spin configurations, which are used to extract coupling constants. Two frequently employed methods of doing this are the dimer fragment approach (DFA) [3,4] and the periodic approach (PA) [3,5].…”

“…The theoretical characterisation and classification of these materials in terms of their dimensionality, the phases they display and their low-energy magnetic behavior is an important part of this investigation. At low energies, the properties of a magnetic material may be mapped onto those of a magnetic spin model [3][4][5][6] (e.g., the Heisenberg model) in which the chemical, structural, and electronic properties underlying its magnetism are encoded in a small number of parameters, such as exchange constants. The diversity of possible structural and chemical arrangements allows for the synthesis of moleculebased compounds whose behavior in this energetic limit corresponds to many different model systems.…”